ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling

TL;DR

ModelingToolkit (MTK) is a symbolic, composable system that transforms equations to produce stable, efficient, and parallelized models, integrating graph algorithms and machine learning for accelerated simulation.

Contribution

MTK introduces a novel, equation-based modeling framework that applies graph transformations for automatic parallelization, index reduction, and surrogate model generation without user code modifications.

Findings

MTK achieves 590x speedup over Modelica on HVAC models.

Automated graph algorithms improve model stability and performance.

Surrogate models outperform traditional solvers in accuracy and speed.

Abstract

Getting good performance out of numerical equation solvers requires that the user has provided stable and efficient functions representing their model. However, users should not be trusted to write good code. In this manuscript we describe ModelingToolkit (MTK), a symbolic equation-based modeling system which allows for composable transformations to generate stable, efficient, and parallelized model implementations. MTK blurs the lines of traditional symbolic computing by acting directly on a user's numerical code. We show the ability to apply graph algorithms for automatically parallelizing and performing index reduction on code written for differential-algebraic equation (DAE) solvers, "fixing" the performance and stability of the model without requiring any changes to on the user's part. We demonstrate how composable model transformations can be combined with automated data-driven surrogate generation techniques, allowing machine learning methods to generate accelerated approximate models within an acausal modeling framework. These reduced models are shown to outperform the Dymola Modelica compiler on an HVAC model by 590x at 3\% error. Together, this demonstrates MTK as a system for bringing the latest research in graph transformations directly to modeling applications.